Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
802 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21448649 | C2 | semidirect |
| 2. #21446656 | C2 | semidirect |
| 3. #21445763 | C2 | semidirect |
| 4. #21444335 | C2 | semidirect |
| 5. #21443724 | C2 | semidirect |
| 6. #21443704 | C2 | semidirect |
| 22. C2×AGL(1,ℤ/8)×C61 | C4 | semidirect |
| 27. C61×#417 | C4 | semidirect |
| 57. C22×D4×C61 | C2×C4 | semidirect |
| 64. C2×M16×C61 | C2×C4 | semidirect |
| 69. C2×C4⋊C4×C61 | C2×C4 | semidirect |
| 165. D4×C61 | #99 | semidirect |
| 247. C2×AGL(1,ℤ/8) | Dic61 | semidirect |
| 254. #417 | Dic61 | semidirect |
| 267. C61 | #9365 | semidirect |
| 276. C22×D4 | C2×Dic61 | semidirect |
| 285. C2×M16 | C2×Dic61 | semidirect |
| 292. C2×C4⋊C4 | C2×Dic61 | semidirect |
| 404. D4 | #14519692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448649 | 2 |
| #21446656 | 2 |
| #21445763 | 2 |
| #21444335 | 2 |
| #21443724 | 2 |
| #21443704 | 2 |
| C61×#3006 | 2 |
| #9365 | 61 |